Systems and methods are disclosed for valuating financial contracts and assessing the risk associated with such contracts. Such systems and methods receive valuation details and an internal contract representation related to the contract to value the contract. Internal contract representations describe the contract in terms of flow sets, cash flow functions, and choice functions Choice functions involve determining whether or not the information desirable to make the choice is available when the choice is to be made. If the information is not known for a particular choice function, then the choice function is replaced with a trigger rule. Trigger rules are determinable when the choice has to be made. Trigger rules are based on stochastic processes associated with the choice function.
Legal claims defining the scope of protection, as filed with the USPTO.
1. A method that estimates an expected value of a financial contract, the method performed by a processor programmed to perform the steps of the method and comprising: receiving, at the processor, valuation details for valuation of the contract, the valuation details comprising: one or more particular financial models that are used for valuation of the contract; and a set of stochastic variables within the one or more particular financial models which are treated stochastically for estimating the expected value of the contract; receiving, at the processor, an internal contract representation and storing the internal contract representation in a memory accessible to the processor, the internal contract representation comprising: one or more flow sets, each flow set comprising one or more cash flow functions, each cash flow function representing an actual cash flow amount at a cash flow time, where at least one cash flow function is modeled, at least in part, by at least one of the one or more particular financial models comprising at least one of the set of stochastic variables; one or more choice functions, each choice function representing a choice between a plurality of choice branches at a corresponding choice time, each choice branch comprising at least one of: a downstream flow set; and a downstream choice function; estimating, by the processor, the expected value for the contract, where estimating the expected value for the contract comprises: identifying, by the processor, a downstream choice function within the internal contract representation, the downstream choice function forming at least a part of one of the choice branches of a first choice function within the internal contract representation, the first choice function representing a choice between a first plurality of choice branches at a first choice time, and the downstream choice function representing a choice between a second plurality of choice branches at a downstream choice time, the first choice time preceding the downstream choice time; for the purpose of estimating the expected value of the contract, replacing, by the processor, the downstream choice function within the internal contract representation stored in the memory with a trigger rule, the trigger rule evaluated based on information known at the first choice time, the trigger rule specifying one of the choice branches of the downstream choice function when evaluated, and the trigger rule based on one or more explanatory stochastic processes selected from the set of stochastic variables which model a cash flow function present in at least one of the choice branches of the downstream choice function; for a plurality of iterations: generating, by the processor, a valuation set which specifies one value for each of the stochastic variables within the set of stochastic variables, where generating the valuation set comprises, for each stochastic variable within the set of stochastic variables, generating a random draw based on a distribution of the stochastic variable, the random draw representing the one value for the stochastic variable within the valuation set; evaluating, by the processor, the trigger rule based on a portion of the valuation set comprising stochastic variables whose values are known at or before the first choice time; specifying, by the processor, one of the choice branches of the downstream choice function based on the evaluation of the trigger rule; determining, by the processor, an iteration contract value based on the internal contract representation having the downstream choice function replaced by the trigger rule and at least a portion of the valuation set and based on the one of the choice branches of the downstream choice function specified by evaluation of the trigger rule; determining, by the processor, the expected value of the contract to be an average of the iteration values of the contract over the plurality of iterations; and saving the expected value of the contract in the memory.
2. The method according to claim 1 , where estimating the expected value for the contract comprises repeating the step of replacing the downstream choice function with a trigger rule, until the internal contract representation no longer includes any choice functions having downstream choice functions in their corresponding choice branches.
3. The method according to claim 1 , where the one or more explanatory stochastic processes on which the trigger rule is based comprise all of the set of stochastic variables which model the cash flow function presented in at least one of the choice branches of the downstream choice function.
4. The method according to claim 1 , where replacing the downstream choice function with the trigger rule comprises: using the one or more explanatory processes to generate one or more explanatory contracts; and for each of the one or more explanatory contracts, estimating an expected value of the explanatory contract.
5. The method according to claim 4 , where using the one or more explanatory processes to generate one or more explanatory contracts comprises generating one or more internal explanatory contract representations, each internal explanatory contract representation comprising one or more explanatory flow sets, each explanatory flow set comprising one or more explanatory cash flow functions, each explanatory cash flow function representing an actual explanatory cash flow amount at an explanatory cash flow time, where at least one explanatory cash flow function is modeled, at least in part, by at least one of the one or more particular financial models comprising at least one of the set of stochastic variables.
6. The method according to claim 5 , where at least one of the internal explanatory contract representations comprises one or more explanatory choice functions, each explanatory choice function representing a choice between a plurality of explanatory choice branches at a corresponding explanatory choice time, each explanatory choice branch comprising at least one of: a downstream explanatory flow set; and a downstream explanatory choice function.
7. The method according to claim 4 , where estimating the expected value of the explanatory contract involves a procedure substantially similar to that of estimating the expected value for the contract, except that the explanatory contract is used in place of the contract.
8. The method according to claim 4 , where the one or more explanatory contracts comprise at least one explanatory contract that is a product of a plurality of other explanatory contracts.
9. The method according to claim 8 , where each of the other explanatory contracts is generated on a basis of at least one different one of the one of the explanatory processes.
10. The method according to claim 4 , where replacing the downstream choice function with the trigger rule comprises: generating the trigger rule, the trigger rule comprising an evaluated trigger argument, the trigger argument based, at least in part, on the one or more explanatory contracts.
11. The method according to claim 10 , where the trigger argument comprises a linear combination of the one or more explanatory contracts.
12. The method according to claim 11 , where the trigger argument comprises an offset in addition to the linear combination of the one or more explanatory contracts.
13. The method according to claim 10 , where generating the trigger rule comprises: formulating the trigger argument as a function of the one or more explanatory contracts and one or more unknowns; and regressing the plurality of choice branches of the downstream choice function against the explanatory contracts that solves for the one or more unknowns.
14. The method according to claim 13 , where regressing the plurality of choice branches of the downstream choice function against the explanatory contracts comprises performing a least squares regression.
15. The method according to claim 1 , where each cash flow function specified by cash flow parameters comprising: the cash flow time, a currency of the cash flow, a notional amount of the cash flow and a direction of the cash flow which specifies whether the cash flow is incoming or outgoing.
16. The method according to claim 15 , where the cash flow parameters comprise a rule comprising a mathematical function which prescribes a mapping between the notional amount of the cash flow and the actual cash flow amount.
17. The method according to claim 1 , where each of the one or more choice functions comprises either: a choose highest function representing a direction to choose an option with a highest expected value for a contract holder from among its corresponding plurality of choice branches; and a choose lowest function representing a direction to choose an option with a lowest expected value for the contract holder from among its corresponding plurality of choice branches.
18. The method according to claim 1 , where the valuation details comprise a valuation time at which the contract is valuated.
19. The method according to claim 18 , where estimating the expected value for the contract comprises parsing the internal contract representation into a set of contract valuation functions, the set of contract valuation functions comprising an ultimate contract valuation function representative of a value of the contract and where, for each of the plurality of iterations, determining the iteration contract value comprises evaluating the ultimate contract valuation function.
20. The method according to claim 19 , where parsing the internal contract representation into the set of contract valuation functions comprises processing the internal contract representation to insert one or more discount factor models into the internal contract representation for one or more corresponding cash flow functions having cash flow times that occur after the valuation time, the one or more discount factor models selected from among the one or more particular financial models.
21. The method according to claim 19 , where parsing the internal contract representation into the set of contract valuation functions comprises processing the internal contract representation to insert, into the internal contract representation, values for one or more non-stochastic variables within the one or more particular financial models.
22. The method according to claim 19 , where parsing the internal contract representation into the set of contract valuation functions comprises converting the internal contract representation into the set of contract valuation functions, each valuation function comprising a constant or a computational function having a set of inputs and where the set of contract valuation functions comprises an ordered list of valuation functions for which the set of inputs for any individual valuation function is restricted to: outputs of preceding valuation functions in the ordered list; non-stochastic variables within the one or more particular financial models; and the set of stochastic variables within the one or more particular financial models.
23. The method according to claim 19 , where estimating the expected value for the contract comprises, for each of the plurality of iterations, evaluating one or more of the contract valuation functions using the valuation set, the one or more of the contract valuation functions including the ultimate contract valuation function.
24. The method according to claim 23 comprising: generating a set of contract valuation risk functions corresponding to the set of contract valuation functions, each of the set of contract valuation risk functions comprising one or more partial derivatives of a corresponding contract valuation function with respect to all inputs to the corresponding contract valuation function; and estimating one or more expected values for risk of the contract, each expected value for the risk of the contract comprising an expected value for one of the contract valuation risk functions corresponding to the ultimate contract valuation function; and where estimating the expected value for the risk of the contract comprises, for each of the plurality of iterations, evaluating one or more of the contract valuation risk functions using the valuation set generated during the iteration.
25. The method according to claim 19 comprising: generating a set of contract valuation risk functions corresponding to the set of contract valuation functions, each of the set of contract valuation risk functions comprising one or more partial derivatives of a corresponding contract valuation function with respect to all inputs to the corresponding contract valuation function; and estimating one or more expected values for risk of the contract, each expected value for the risk of the contract comprising an expected value for one of the contract valuation risk functions corresponding to the ultimate contract valuation function.
26. The method according to claim 1 , where generating the random draw based on the distribution of the stochastic variable comprises: generating a random from within a uniform distribution in a range [0,1]; and using the random and the distribution of the stochastic variable to generate the random draw.
27. The method according to claim 1 , where generating the random draw based on the distribution of the stochastic variable comprises at least one of: generating a pseudo random number; and generating a quasi random number.
28. The method according to claim 1 , where generating the valuation set comprises, for at least one of the stochastic variables within the set of stochastic variables, modifying the random draw to conform with a serial correlation which specifies how a value of the stochastic variable depends on temporally previous values of the stochastic variable, where modifying the random draw to conform with the serial correlation is performed prior to the random draw representing the one value for the stochastic variable within the valuation set.
29. The method according to claim 1 where generating the valuation set comprises, for at least one of the stochastic variables within the set of stochastic variables, modifying the random draw to conform with a cross correlation which specifies how a value of the stochastic variable depends on one or more values of another different stochastic variable within the set of stochastic variables, where modifying the random draw to conform with the cross correlation is performed prior to the random draw representing the one value for the stochastic variable within the valuation set.
30. The method according to claim 1 comprising determining a standard deviation of the value of the contract to be the standard deviation of the iteration values of the contract over the plurality of iterations.
31. A computer program product comprising a set of instructions embodied on a non-transitory computer readable medium, the instructions when executed by a processor, cause the processor to perform a method for estimating an expected value of a financial contract, the method comprising: receiving, at the processor, valuation details for valuation of the contract, the valuation details comprising: one or more particular financial models to be used for valuation of the contract; and a set of stochastic variables within the one or more particular financial models which are treated stochastically for estimating the expected value of the contract; receiving, at the processor, an internal contract representation and storing the internal contract representation in a memory accessible to the processor, the internal contract representation comprising: one or more flow sets, each flow set comprising one or more cash flow functions, each cash flow function representing an actual cash flow amount at a cash flow time, where at least one cash flow function is modeled, at least in part, by at least one of the one or more particular financial models comprising at least one of the set of stochastic variables; one or more choice functions, each choice function representing a choice between a plurality of choice branches at a corresponding choice time, each choice branch comprising at least one of: a downstream flow set; and a downstream choice function; estimating, by the processor, the expected value for the contract, where estimating the expected value for the contract comprises: identifying, by the processor, a downstream choice function within the internal contract representation, the downstream choice function forming at least a part of one of the choice branches of a first choice function within the internal contract representation, the first choice function representing a choice between a first plurality of choice branches at a first choice time, and the downstream choice function representing a choice between a second plurality of choice branches at a downstream choice time, the first choice time preceding the downstream choice time; for the purpose of estimating the expected value of the contract, replacing, by the processor, the downstream choice function within the internal contract representation stored in memory with a trigger rule, the trigger rule evaluated based on information known at the first choice time, the trigger rule specifying one of the choice branches of the downstream choice function when evaluated, and the trigger rule based on one or more explanatory stochastic processes selected from the set of stochastic variables which model a cash flow function present in at least one of the choice branches of the downstream choice function; for a plurality of iterations: generating, by the processor, a valuation set which specifies one value for each of the stochastic variables within the set of stochastic variables, where generating the valuation set comprises, for each stochastic variable within the set of stochastic variables, generating a random draw based on a distribution of the stochastic variable, the random draw representing the one value for the stochastic variable within the valuation set; evaluating, by the processor, the trigger rule based on a portion of the valuation set comprising stochastic variables whose values are known at or before the first choice time; specifying, by the processor, one of the choice branches of the downstream choice function based on the evaluation of the trigger rule; determining, by the processor, an iteration contract value based on the internal contract representation having the downstream choice function replaced by the trigger rule and at least a portion of the valuation set and based on the one of the choice branches of the downstream choice function specified by evaluation of the trigger rule; determining the expected value of the contract to be an average of the iteration values of the contract over the plurality of iterations; and saving the expected value of the contract in the memory.
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August 9, 2012
April 14, 2020
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